The width of a rectangular playground is 2x -5 feet and the length is 3x+9 feet write the polynomials that represent the area and the perimeter of the playground
Accepted Solution
A:
Answer:Part 1) [tex]A(x)=6x^{2} +3x-45[/tex]Part 2) [tex]P(x)=10x+8[/tex]Step-by-step explanation:LetL -----> the length of a rectangular playgroundW ---> the width of a rectangular playgroundwe have[tex]W=(2x-5)\ ft[/tex][tex]L=(3x+9)\ ft[/tex]step 1Find the area of the playgroundThe area of a rectangle is equal to[tex]A=LW[/tex]substitute the given values[tex]A(x)=(3x+9)(2x-5)\\A(x)=6x^{2} -15x+18x-45\\A(x)=6x^{2} +3x-45[/tex]step 2Find the perimeter of the playgroundThe perimeter of a rectangle is equal to[tex]P=2(L+W)[/tex]substitute the given values[tex]P(x)=2((3x+9)+(2x-5))[/tex][tex]P(x)=2(5x+4)[/tex][tex]P(x)=10x+8[/tex]